Beyond the 3rd and the 4th Century,Roman Empire was repeatedly bombarded with Germanic Invaders
That's rather the Vth century you're describing, with groups of Barbarians moving and settling on their own, after negotiating or forcing their way, in Roman provinces. But for the IIIrd and IVth centuries, Barbarians essentially raided down Roman provinces and rarely settled as whole peoples except peripheral regions (Decumate Fields, Dacia) that got abandoned or in the latter part in actually negotiated treaties (as Goths in Moesia, Franks in Toxandria, possibly Saxons in the Saxon Shore).
Rome decides to negotiate with them. The lands of Germanic peoples,
It's pretty much what Romans did : confronted to whole confederations that raided its provinces, they didn't just resorted to military opposition (they lacked the capacity to do that systematically anyway, due to Persian pressure) but managed to pass treaties with Barbarians (rather than "Germanic" which is a bit of an anachronism) on a relatively good position giving the situation.
It took various forms, such as settlement of Barbarians as
laeti (which was a practice, coming from the Augustean period in some early form, of settling whole bands/tribes in roman provinces as military and/or productive workforce), clientelisation, mercenariship and by the late IVth century and especially the Vth century treaties of federation which greatly differed from the other ones by the fact Barbarians obtained regional and territorial autonomy : this happened because Rome negotiated less and less in a good standing.
Power sharing agreements are signed off for this huge territories which now extends up to Central Asia and Scandinavia.
You forget an important factor : what did Barbarians wanted out of Rome. It was not they wanted to compete with Romania as a state and have the freedom to build their own Rome, they wanted in a context of climatic change (which significantly limited autonomous ressource-gathering in Barbaricum and increased economical dependency trough subsides or raiding) to move down in Romania as migrants/raiders at least for what matter limes peoples.
It's not like, either, Romans had not tought intervening politically with Barbaricum : the whole chiefdom-building there was heavily dependent form Roman interaction, would it be trough trade (especially on metals and grain), subsides, alliances (we know Romans sent "military advisors" as far as Poland) and direct interventions.
It's just that creating "others Rome" interested no one, especially not Barbarians.
Population increases steadily.
I doubt that. Romania faced a constant lack of manpower and workforce in its provinces, at least in the western and central ones, which is exactly why they resorted to Barbarian settlement in a large scale enough from the late IIIrd century onward for their military and productive need. You somehow manage to blockade Barbarian groups moving in, you make the problem worse.
The Empire is multilingual with Germanic,Slavic,Scythian,Middle Eastern,Greek,Semitic,Coptic,Caucasian,Celtic,etc. People interested learn others languages. Nobody in Europe and Roman Empire is treated as Barbarian.
You would definitely need something else to make that happened. Latin and Greek were the basic language of the European superpower, any other being provincial at best, Barbarian at worst and steadily declining as soon as it could happen. See, the distinction between Roman and Barbarian wasn't just something prejudiced that with good will and understanding and living together could be dealt with, it was a basic identitarian feature of Roman society : Romans were people living under and with the Roman state with a whole set of rights and clear duties; when Barbarians were defined by the absence of these and the more or less arbitrary rule of a petty-king.
One could jump categories (Romans joining up with Barbarians, Barbarians obtaining Roman citizenship) but the "stigma" of having Barbarian origin never really went off just as it happened with Stilicho and, at least for what mattered Roman warlords, Ricimer.
The sheer weight of Roman culture as not just a language but as well institution, was so important that Barbarians IOTL switched really quickly to bilinguism, diglossy and eventually Latin monolinguism in less than one century after their definitive settlement. Being integrated into Roman state apparatus implies a cultural assymetrical relationship even if the political balance is more favorable to Barbarians.